What is the total amount of potential energy that can be stored in a 10,000 gallon water tower built with the water tank 61.50 m above ground level?
<hint: You will need to look up the mass of a gallon of water in Kilograms>
1 gal. = 8 Lbs. = 3.63 kg.
M = 10,000gal * 3.63kg/gal. = 36,320 kg.
PE = M*g*h = 36,320*9.8*61.5 Joules.
To calculate the total potential energy stored in the water tower, we need to find the potential energy of the water and multiply it by the total mass of the water.
First, let's convert the volume of water in gallons to kilograms. We'll need to look up the mass of a gallon of water in kilograms.
One US gallon of water is approximately 3.78541 liters. And since the density of water is 1 kilogram per liter, we can conclude that the mass of 1 gallon of water is approximately 3.78541 kilograms.
Given that the water tower has a volume of 10,000 gallons, we can multiply the volume by the mass of one gallon to find the total mass of the water in the tower:
Total Mass = Volume × Mass of a Gallon
Total Mass = 10,000 gallons × 3.78541 kilograms/gallon
Now that we have the total mass of the water, we can calculate the potential energy. The potential energy is given by the formula:
Potential Energy = Mass × Gravitational Acceleration × Height
Here, the mass is the total mass of the water, the gravitational acceleration is approximately 9.8 m/s^2, and the height is the height of the water tank above ground level.
Potential Energy = Total Mass × 9.8 m/s^2 × Height
Substituting the values, we have:
Potential Energy = (10,000 gallons × 3.78541 kilograms/gallon) × 9.8 m/s^2 × 61.50 m
Now you can calculate the potential energy by simply plugging in the values into the equation and evaluating it.